Inspired by the example of how background music influences the choice of entree at a restaurant, a statistics student decided to investigate other ways to influence a person’s behavior. Using 60 volunteers, she randomly assigned 20 volunteers to receive a red survey, 20 volunteers to receive a blue survey, and 20 volunteers to receive a control survey. The first three questions on each survey asked, “When you think of the color red, what do you think about?” On the blue survey, the question replaced “red” with “blue.” On the control survey, the last two questions were not about color. As a reward, each volunteer was allowed to choose a chocolate candy in a red wrapper or a chocolate candy in a blue wrapper. The table shows the results of the experiment. Survey Type Red Blue Control Total —————————————— What are appropriate null and alternate hypotheses in this setting? Total 13 5 8 26 Color Blue of candy Total Ho: The proportion who would choose the red candy is 0.33 in all three treatment groups. Ha: The proportion is not 0.33 in all three treatment groups. Ho: The number who choose the red candy is the same as those who choose the blue candy for subjects like these who receive the red survey, the blue survey. Ha: The number who choose the red candy is not the same as those who choose the blue candy for subjects like these who receive the red survey, the blue survey. Ho: The distribution of candy choice is the same for subjects like these who receive the red survey, the blue survey, and the control survey. Ha: The distribution of candy choice is not the same for subjects like these who receive the red survey, the blue survey, and the control survey. Ho: The distribution of candy choice is the same for subjects who received the red survey, the blue survey, and the control survey. Ha: The distribution of candy choice is not the same for subjects like these who received the red survey, the blue survey, and the control survey. Ho: The distribution of candy choice is not the same for subjects like these who receive the red survey, the blue survey, and the control survey. Ha: The distribution of candy choice is the same for subjects like these who receive the red survey, the blue survey, and the control survey.
The Correct Answer and Explanation is:
The correct null and alternative hypotheses in this setting are:
Ho: The distribution of candy choice is the same for subjects who received the red survey, the blue survey, and the control survey.
Ha: The distribution of candy choice is not the same for subjects who received the red survey, the blue survey, and the control survey.
Explanation:
This is an example of a hypothesis test for comparing categorical data between multiple groups. The null hypothesis (Ho) is typically a statement of no effect or no difference, while the alternative hypothesis (Ha) suggests that there is some difference or effect. In this case, the researcher is interested in examining whether the color of the survey (red, blue, or control) affects the candy choice (red or blue wrapper).
The response variable is categorical (whether a participant chose the red or blue candy), and the explanatory variable is also categorical (which survey they received: red, blue, or control). Therefore, a Chi-square test for homogeneity or independence is appropriate for testing if the distribution of candy choices differs based on the type of survey.
The null hypothesis assumes that the distribution of candy choices is the same across the three groups (i.e., the proportion of people who choose the red candy and the proportion who choose the blue candy is the same for participants who receive the red survey, the blue survey, and the control survey). In other words, the survey color has no effect on candy choice.
The alternative hypothesis suggests that the distribution of candy choice is not the same across the three survey types, meaning that the color of the survey does influence the likelihood of selecting one candy over the other.
This hypothesis test will help determine if there is a statistically significant difference in candy choice based on the color of the survey participants received. If the p-value is below the chosen significance level (usually 0.05), the null hypothesis would be rejected, suggesting that the survey color does influence candy choice.
